Many modern engineering analyses are performed with the aid of a computer system. One of such computer aided engineering (CAE) analyses is referred to as discrete element method (DEM) or distinct element method, which is generally used for numerically simulating the motion of a large number of discrete particles. With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of discrete particles. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in crack propagation, granular flows, powder mechanics, and rock mechanics.
The classic mechanics are based on solving Partial Differential Equations (PDEs) over the domain with the assumption of continuous distribution of mass, including finite element methods, boundary integral methods, meshless methods, and so on. In other disciplines, molecular dynamics (MD) have been used for determining the forces and energy atoms and molecules for simulations spanning nano-level to micro-level, which are not suitable for macro-level simulations.
In contrast, DEM offers a different approach that does not require formulation of a PDEs for continuum mechanics. However, there are drawbacks or shortcomings in prior art approaches. In particular, there is no integrated technique to bridge the continuum mechanics and fractured particles after the continuum has been damaged. Many ad hoc methods have been proposed, but none of these prior art approaches is satisfactory. For example, one of the prior art approaches assumes the forces acting on particles are axial only, hence not being able to simulate a domain having any relative shear deformation or lateral deformation correctly.
It would, therefore, be desirable to have systems and methods of providing an improved model amongst a plurality of discrete particles that represents a physical domain made of brittle material in a time-marching simulation to obtain numerically simulated continuum physical phenomena.